This may a be far-fetched, but worth a shot.
It is possible that in the 1871 census, James E Quine, sn of Margaret Quine was using his father's name.
In the 1871 census in Lonan at 26 Laxey Glen, there is a Quine family: John aged 69 Lead miner, Elizabeth wife age 58, Eunice 17 daughter and James Cannon, boarder age 8. His birthplace is given as Onchan.

Elizabeth appears to be Elizabeth Fargher who married John Quine in Lonan on August 11 1832. They could be Margaret's grandparents.
The couple had eight children including Margaret Elizabeth Quine christened on March 22 1840 in Lonan. Margaret Quine does not appear in either the 1861 or the the 1871 census but may have married before 1871.

No birth appears in the IGI for a Manx James Cannon between 1861 & 1865. In the 1871 census there is a family headed by James Cannon 31 Shoemaker, born Ramsey. In the 1881 census in Maughold the family appears again and he is still a shoemaker, age 40, b Ramsey.
It seems possible that James Cannon was
James E Quine's natural father and that he used his granfather's name instead of his fathers.